Butterflies, tornadoes and climate modelling

April 23rd, 2008 by group

Many of you will have seen the obituaries (MIT, NYT) for Ed Lorenz, who died a short time ago. Lorenz is most famous scientifically for discovering the exquisite sensitivity to initial conditions (i.e. chaos) in a simple model of fluid convection, which serves as an archetype for the weather prediction problem. He is most famous outside science for the ‘The Butterfly Effect’ described in his 1972 paper “Predictability: Does the Flap of a Butterfly’s Wings in Brazil Set Off a Tornado in Texas?”. Lorenz’s contributions to both atmospheric science and the mathematics of dynamical systems were wide ranging and seminal. He also directly touched the lives of many of us here at RealClimate, and both his wisdom, and quiet personal charm will be sorely missed.

Ed Lorenz had a reputation of being shy and quiet, and this was indeed the impression he gave on first meeting. Indeed raypierre was interviewed by Ed at MIT in 1979 for his first faculty job — and remembers having to ask most of the questions as well as answer them. But he also remembers a lot of timely support from Ed that helped smooth over the somewhat rocky transition from basic turbulence theory to atmospheric science. The longer you were around Ed, the more you came to appreciate his warmth and sense of humor. He was an avid hiker, and many in the community (our own Mike Mann included) have recollections of time on the trail with him around the hills of Boulder and elsewhere.

Lorenz launched the modern era of the study of chaotic systems, which has profound implications both within and beyond atmospheric science. We’ll say more about that in a bit, but the monumental work on chaos should not leave Lorenz’s other contributions to atmospheric science completely in its shadow. For example, in a 1956 MIT technical report, Ed introduced the notion of “empirical orthogonal functions” to atmospheric science, and this technique now plays a central role in diagnostic studies of the atmosphere-ocean system. He also pioneered the study of angular momentum transport in the atmosphere, and of atmospheric energetics. Among other things, he introduced the important notion of “available potential energy,” which quantifies the fact that not all of the potential energy can be tapped by allowable rearrangements of the atmosphere. Later, he pioneered the concept of resonant triad instability of atmospheric waves, an idea that has repercussions for the sources of atmospheric low frequency variability. As if that weren’t enough Ed also introduced the concept of the “slow manifold” — a special subset of solutions to a nonlinear system which evolve more slowly than most solutions. The atmospheric equations support a lot of very quickly changing solutions, like sound waves and gravity waves, but on the whole what we think of as “weather” or “climate” involves more ponderous motions evolving on time scales of days to years. Ed’s work on this subject launched the study of how such slowly evolving solutions can exist, and how to initialize a numerical model so as to minimize the generation of the fast transients. This is now part and parcel of the whole apparatus of data assimilation and numerical weather forecasting.

Ed was not a user of general circulation models. His essential approach was to crystallize profound phenomena into very small sets of equations for how a handful of variables change with time. He left behind him a dozen or so such models, each of which would repay many lifetimes of study. He was indeed a master of “seeing the world in a grain of sand.” You can read about some of these models in the talk raypierre gave at the 1987 Lorenz ‘retirement’ symposium — not that this slowed him down!

Now let’s take a closer look at that butterfly effect. Despite the fact that there are no butterflies or tornadoes in climate models, Lorenz’s discoveries and their implications played a central role in climate modelling efforts and in the most recent IPCC report.